# Newton's Gravity and Escape Velocity

1. How would you describe the "use of Newton's gravity to hold the solar system together" to an elementary school child? Give some examples and situations that you might find helpful in describing gravity.

2. What is gravity? Describe gravity throughout the universe.

3. What is escape velocity? Is it the same everywhere? Why or why not?

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1. How would you describe the "use of Newton's gravity to hold the solar system together" to an elementary school child? Give some examples and situations that you might find helpful in describing gravity.

The English physicist Isaac Newton introduced the term "gravity" after he saw an apple falling onto the ground in his garden and later proposed that gravity was just a particular case of gravitation. Newton's Law of Universal Gravitation states that every particle in the universe exerts a force on every other particle along the line joining their centres. The magnitude of the force is directly proportional to the product of the masses of the two particles, and inversely proportional to the square of the distances between them. In mathematical terms the force of gravitation is written as

F=GMm / R^2 ------------------------- (1)

where M and m are masses of two bodies, R is the distance between them and G is called the Gravitational Constant.

Every body on the surface of the Earth exerts a gravitational force on every other and also an equal force is exerted by Earth on them. If we are expanding this up to Sun, then Sun is also applying a gravitational force on Earth and every object on it. But the strength of the force varies. The gravitational force between Sun and Earth is more than that between Sun and a human being. This is because of the difference in the product of masses(here the distance between them is same). We can prove it by substituting the values in equation (1).

Msun = 1.98892 Ã— 10^30 kilograms

Mearth = 5.9742 Ã— 10^24 kilograms

Mhuman = 65 kilograms

R = 1.4959 x 10^11 metres

G = 6.6726 x 10^-11 m^3 kg^-1 s^-2

Force between Sun and Earth is F(s.e) = 3.543 x 10^22 Newton

Force between Sun and Human being is F(s.h) = 0.3854 Newton

The Sun is the centre of our solar system which contains more than 99.8% of all the mass in the solar system. Its size gives it the gravity it needs to hold the solar system together. The sun's gravity pulls the objects down while they keep trying to move away. It's a never-ending tug-of-war that keeps the planets in their orbits instead of flying off into space. When you have two very large objects like the Moon and the Earth, different parts of them are pulled(gravitational pull) differently due to distance. The part of the Earth closest to the moon is pulled most. If there are oceans there, they will bulge out. The middle of the Earth is not pulled as strongly towards the moon, but it still is pulled more than the water on the far surface of the Earth. The far side of the Earth is pulled least, making another bulge on the far side of the Earth. As the Earth rotates underneath these bulges, we experience two high tides per day. Orbits are the result of a perfect balance between the forward motion of a body in space, such as a planet or moon, and the pull of gravity on it from another body in space, such as a large planet or star. These forces of inertia and gravity have to be perfectly balanced for an orbit to happen. Some daily examples of gravity are: When you throw a ball up in the air, it always comes back down. When you jump rope, the rope doesn't stay above our heads in the air. When you fall, gravity pushes you to the ground resulting in scrapes and burns.

2. What is gravity? Describe gravity throughout the universe.

Gravity is a force of attraction that exists between any two masses, any two bodies, any two particles. Gravity is not just the attraction between objects and the Earth. The strength of the force is proportional to the product of the two masses of the bodies and inversely proportional to the square of the distance between the two bodies. The mass of the earth attracts you and, likewise, you attract the earth. It is an attraction that exists between all objects, everywhere in the Universe. Sir Isaac Newton discovered that a force is required to change the speed or direction of movement of an object. He also realized that the force called "gravity" must make an apple fall from a tree, or humans and animals live on the surface of our spinning planet without being flung off. Newton's law of gravity is a mathematical description of the way bodies are observed to attract one another. Mathematically speaking, the force of attraction between two bodies of mass m1 and m2 separated by a distance of r is given by

F=GMm / R^2

where G is called the Gravitational Constant. It has a value of 6.6726 x 10^-11 m^3 kg-1 s-2.

Gravity extends throughout the universe making it a function of the universe not just simply the force that holds us to the ground. The effect of gravity extends from each object out into space in all directions, and for an infinite distance. However, the strength of the gravitational force reduces quickly with distance. Humans are never aware of the Sun's gravity pulling them, because the pull is so small at the distance between the Earth and Sun. The Sun's gravity that keeps the Earth in its orbit and the Moon's gravity is responsible for the ocean tides on Earth.

3. What is escape velocity? Is it the same everywhere? Why or why not?

Escape velocity is the initial velocity needed for an object to escape from the gravitational pull of the Earth, that is to escape the Earth without falling back. Gravitational force diminishes as distance from the centre of the Earth increases. When we are throwing an object upwards it will stop and start to return at a point where its negative acceleration of gravity(-g) becomes zero. To escape from the Earth's gravitational field the object must have greater energy than its gravitational binding energy. The gravitational potential energy between an object of mass 'm' and a planet of mass 'M' separated by a distance of 'R' is given by GMm/R. The kinetic energy of the object moving upward with a velocity 'v' is given by (mv^2)/2. When one object is escaping, its kinetic energy should be equal to the gravitational potential energy. That means

(mv^2)/2 = GMm/R

Escape velocity v = (2GM/R)^1/2 -----------------------(2)

Note that the inertial mass of the object has cancelled, so that the escape velocity of any object is independent of its mass. This means that if you want to throw a grain of rice or an elephant into outer space, you need to give them both the same initial velocity. On the surface of the Earth, the escape velocity is about 11.2 kilometres per second (~6.96 miles/s), which is approximately 34 times the speed of sound.

No, the escape velocity is not the same everywhere. From the equation (2) it is clear that the escape velocity depends on M and R. For example an object on the surface of Sun needs an escape velocity of 617.5 km/s while on Mercury it needs 4.4 km/s. That means the escape velocity depends upon the heavy mass where the object is and also the distance between them.

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